Nodal Cooper-pair stabilized phase dynamics in granular d-wave superconductors

Scanning tunneling microscope measurements on single crystals of Bi2Sr2CaCu2O8+x materials have shown that the d-wave superconductivity in cuprates has nanoscale inhomogeneities and is still robust in spite of their presence. We study the dynamics of Josephson coupling between such granular d-wave superconductors, focusing on the effect of nodal Cooper pairs and disorder. We find that the nodal Cooper pairs give rise to a power-law Josephson coupling which leads to the stabilization of the superconducting phase. Our findings suggest that the d-wave superconductivity in an array of grains is unexpectedly robust against a disordering transition, as observed in the experiments. Furthermore, we predict the existence of a planar Josephson-plasmon mode with characteristic frequency that decreases with temperature.